Abstract
We present a simple, arithmetic-free, efficient scheme to compress trees maintaining the nearest common ancestor (NCA) information. We use this compression scheme to provide an O(n + q lg lg n) solution for solving the NCA problem on Pure Pointer Machines (PPMs) (i.e., pointer machines with no arithmetic capabilities) in both the static and dynamic case, where n is the number of add-leaf/delete operations and q is the number of NCA queries. This solution is optimal.
Research is supported by NSF grants CCR-9900320, EIA-0130887, CCR-9875279, CCR-9820852, and EIA-9810732.
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References
S. Alstrup and M. Thorup. Optimal Pointer Algorithms for Finding Nearest Common Ancestors in Dynamic Trees. Journal of Algorithms, 35:169–188, 2000.
A.M. Ben-Amram. What is a Pointer Machine? In SIGACT News, 26(2), 1995.
M.A. Bender and M. Farach-Colton. The LCA Problem Revisited. In Proceedings of LATIN 2000, pages 88–94. Springer Verlag, 2000.
A.L. Buchsbaum et al. Linear-Time Pointer-Machine Algorithms for Least Common Ancestors. In Procs. ACM STOC, ACM Press, 1998.
R. Cole and R. Hariharan. Dynamic LCA Queries on Trees. In Proceedings of the Symposium on Discrete Algorithms (SODA), pages 235–244. ACM/SIAM, 1999.
A. Dal Palù, E. Pontelli, D. Ranjan. An Optimal Algorithm for Finding NCA on Pure Pointer Machines. NMSU-TR-CS-007/2001, http://www.cs.nmsu.edu, 2001.
H.N. Gabow and R. E. Tarjan A linear-time algorithm for a special case of disjoint set union J. Comput. System Sci 30 (1985), 209–221.
D. Gusfield. Algorithms on Strings, Trees, and Sequences. Cambridge Press, 1999.
D. Harel and R.E. Tarjan. Fast Algorithms for Finding Nearest Common Ancestor. SIAM Journal of Computing, 13(2):338–355, 1984.
E. Pontelli and D. Ranjan. A Simple Optimal Solution for the Temporal Precedence Problem on Pure Pointer Machines. TR-CS-006/2001, New Mexico State U., 2001.
E. Pontelli and D. Ranjan. Ancestor Problems on Pure Pointer Machines. In LATIN, 2002.
D. Ranjan et al. An Optimal Data Structure to Handle Dynamic Environments in Non-deterministic Computations. Computer Languages, (to appear).
D. Ranjan, E. Pontelli, L. Longpre, and G. Gupta. The Temporal Precedence Problem. Algorithmica, 28:288–306, 2000.
B. Schieber and U. Vishkin. On Finding Lowest Common Ancestors. SIAM J. Comp., 17:1253–1262, 1988.
A. Tsakalidis. Maintaining Order in a Generalized Linked List. ACTA Informatica, (21):101–112, 1984.
A.K. Tsakalidis. The Nearest Common Ancestor in a Dynamic Tree. ACTA Informatica, 25:37–54, 1988.
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Dal Palú, A., Pontelli, E., Ranjan, D. (2002). An Optimal Algorithm for Finding NCA on Pure Pointer Machines. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_44
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DOI: https://doi.org/10.1007/3-540-45471-3_44
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